⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⡠⢀⠄⡠⢀⠄⠠⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠰⢀⠆⡡⢂⡱⣈⢦⠱⣌⢦⡱⣌⢬⡑⢆⡒⠤⣁⢂⠐⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡈⡔⢌⠢⡜⡤⣎⣵⣯⣶⣿⣾⣿⡾⣷⢿⡾⣧⣿⣮⣗⣧⡲⣌⡒⣄⠢⡈⠔⡀⢂⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣠⠚⡰⢡⣎⣷⣽⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠑⢫⡞⡵⣋⠷⡙⢦⢳⡜⡤⡑⠢⢌⡐⠠⢁⠠⠀⢠⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⣀⢋⢤⣳⣽⣿⣿⣿⣿⠟⢡⡀⢆⡔⢡⠈⠄⠀⠀⠀⠀⠀⢸⣷⣛⢶⡱⢢⠍⡂⠆⡈⠱⠩⢳⠤⣌⠱⣀⠆⡏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⡰⢑⡤⣯⣾⣿⣿⢿⣻⡿⢁⣎⡶⣽⢋⠜⠂⠄⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⢁⠋⠌⡑⢂⠰⢁⠒⢢⠋⠘⠳⡜⠛⡀⠁⠀⡀⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢠⡘⢴⣫⣾⣿⡿⡟⠞⢫⡟⢡⢎⡼⡝⢢⠁⢊⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠠⡉⡜⣑⠚⠲⠡⠞⠁⠒⡔⠐⡈⠐⠀⠀⡐⢄⠂⠀⠈⠀
⠀⠀⠀⠀⠀⠠⠈⠠⡁⠜⢢⡼⣿⠿⠛⢉⠠⣐⡬⠉⠀⠀⠈⡐⠉⠂⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣷⡥⣾⣣⡙⠤⡑⠢⠐⠀⢀⠢⠁⠂⠀⣮⠑⡌⠄⡁⠀⠀
⠀⠀⠀⠀⠀⠄⢂⠡⡘⢌⠷⠋⢁⣤⢶⣞⣿⣿⣿⠀⠀⢈⠻⡝⢒⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣞⡷⣓⢦⡙⢣⡄⢡⠠⣉⠇⡀⠂⢀⠐⠨⢳⢌⠒⠠⠀⠀
⠀⠀⠀⠀⠀⡐⠠⢂⠑⣨⣴⡾⣟⢾⣋⠞⣹⣞⡿⡆⠀⠀⠤⠐⠋⠁⠉⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⣿⣹⠖⣭⢒⡜⢤⡛⢁⠈⠀⠀⠄⠠⠀⠱⢪⡑⠌⡐⠀
⠀⠀⠀⠀⠀⠄⡡⢆⣿⡟⣧⡛⣵⢺⡔⣮⢱⣊⣿⡅⡄⠀⠀⠀⠤⣤⠀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⡟⣲⢯⡜⣦⢃⠀⠀⣄⠃⠌⠠⠐⠀⠳⣘⠰⢀⠀
⠀⠀⠀⠀⠌⢢⠑⣮⠷⢚⡔⡻⠈⢦⠙⣀⠣⡙⢮⠇⣿⠀⠀⠀⠀⠀⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠻⡇⠀⢀⡞⡤⢊⡔⢁⠠⠀⠱⣌⠒⡄⠂
⠀⠀⠀⠌⠰⡁⢞⣼⢋⠔⠈⠁⠜⢂⠰⢀⠲⣉⠎⣧⢻⠀⠀⠀⠀⠀⠈⠑⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡝⠀⠀⠊⠝⡳⠃⠐⡂⠄⠐⠀⣎⠱⢠⠁
⠀⠀⠀⠌⣂⠱⢪⣽⠂⠀⠁⠈⠀⠀⠂⠈⢡⠘⡜⢦⢛⡄⠀⠀⠀⠀⠀⠄⠀⠢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⢁⢂⠈⡀⠰⣌⠳⢠⠈
⠀⠀⠈⡔⢠⢉⢧⣻⠄⠀⠀⠀⠀⠀⠀⡁⠂⠌⡘⠤⢋⢦⠀⡂⠀⠀⢈⠆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⢄⡞⠀⢀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠲⡀⢂
⠀⠀⠐⡀⠆⡌⢲⡽⡂⠀⠀⠀⠀⠀⠁⠠⠈⠐⠠⡑⢌⣚⠀⡇⠀⠀⢬⡘⠁⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⢠⠞⠀⠀⠲⣙⡆⠀⠀⠀⠀⠀⠀⠡⠈⢐⢊⠒⡁⠄
⠀⠀⠐⠠⠘⡠⢃⡞⣇⠀⠀⠀⠀⠀⠀⠀⠐⠈⠄⡐⣈⢾⠀⠀⠀⠐⢂⠀⡀⠡⠀⢐⡀⠀⠀⠀⠀⠀⠀⢀⠐⢠⠋⠀⠀⠀⣁⠒⠀⠄⠀⠀⠀⠀⠀⠐⠀⠏⢎⡁⢂⠐
⠀⠀⠀⡁⠂⠱⠨⣜⡹⡄⠀⠀⠀⠀⠀⠀⠐⠀⠠⠠⡱⠞⠀⠀⠀⠘⠀⠐⡈⢄⡉⡀⠄⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠐⠀⠂⡌⠀⠀⠀⠀⠀⠠⢀⡹⢍⡒⠌⣀⠂
⠀⠀⠀⢀⠡⠈⡅⢢⠝⣱⡀⠀⠀⠀⠀⢈⠀⠂⢀⠁⢴⠋⠀⠀⠀⠀⠀⠀⠈⢀⠰⠜⢤⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢈⠒⡄⢀⠀⠀⠀⠀⠀⢄⠻⡜⢌⠐⡀⠀
⠀⠀⠀⠀⠠⠁⡄⠃⡜⣡⢷⡀⠀⠀⠀⠀⠐⠠⠀⣌⡎⠀⢀⢠⠐⡀⢂⡀⠀⠀⠠⠦⠀⠑⠄⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠠⢩⠔⠂⠀⠀⠀⠀⠀⡈⠷⣈⠆⢂⠀⠀
⠀⠀⠀⠈⠀⠡⣀⠣⢐⠡⡞⣹⢆⡀⠁⠠⢈⠐⡰⢦⣁⡎⢌⠒⡉⢀⠁⠀⠀⠀⠀⠀⠀⠄⠈⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡜⠀⠀⠀⠀⠀⠀⢀⠳⡐⢈⠀⢀⠀
⠀⠀⠀⠀⠀⠁⠄⠂⡌⢢⠙⣬⢛⢦⣅⠢⢌⢼⡹⠏⡰⠈⠄⠃⠤⢈⠈⠁⠀⠀⠀⠀⠀⠀⠁⠂⡀⠈⢤⠀⠀⠀⠀⠀⠀⠀⠐⡨⢄⠠⠀⠀⠀⠀⠀⠀⠣⢁⠂⠄⠀⠠
⠀⠀⠀⠀⠀⠐⢈⡐⠨⠄⡋⢤⢋⡖⢮⢷⡾⠎⠐⠀⠁⣀⠀⠁⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡙⠖⡆⡄⢀⠀⠀⡀⡑⡀⢀⠀⠀⠀⠀⠀⠀⠐⠠⢈⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠂⠄⢡⠂⣉⠦⣩⠼⣭⡟⠡⠈⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⡐⠈⢒⠉⠎⢎⠑⠲⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠡⢈⠄⡘⢄⡊⡔⠹⠁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⢀⠐⠈⢀⠁⠂⠈⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⢀
⠀⠀⠀⠄⠀⠀⠀⠈⠢⡑⢂⡐⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠈⡀⠂
⠀⠀⠀⠈⠰⢀⠀⠁⡐⢈⠡⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡐⠠⠀⠀
⠀⠀⠀⠀⠀⠈⠢⡁⠀⠄⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀
⠀⠀⠀⠀⠀⠁⢂⡈⠡⠌⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠄⡐⠈⠁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⡤⢤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣼⡅⠠⢀⡈⢀⣙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⠀⠀⠀⠈⠙⠿⣝⢇⠀⠀⣀⣠⠤⠤⠤⠤⣤⡤⠚⠁⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢧⡀⠀⠀⠠⣄⠈⢺⣺⡍⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⡆⢀⠘⣔⠄⠑⠂⠈⠀⡔⠤⠴⠚⡁⠀⠀⢀⠀⠀⠀⣠⠔⢶⡢⡀⠀⠠⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣇⠀⢃⡀⠁⠀⠀⠀⡸⠃⢀⡴⠊⢀⠀⠀⠈⢂⡤⠚⠁⠀⠀⠙⢿⠀⠉⡇⠀⠀⠀⠀⠀
⠀⠀⠀⣠⠾⣹⢤⢼⡆⠀⠀⠀⠀⠀⠀⠈⢀⠞⠁⠀⢠⣴⠏⠀⠀⠀⠀⠀⠀⠸⡇⠀⢇⠀⠀⠀⠀⠀
⠀⠀⣾⢡⣤⡈⠣⡀⠙⠒⠀⠀⠀⠀⣀⠤⠤⣤⠤⣌⠁⢛⡄⠀⠀⠀⠀⠀⠠⡀⢇⠀⠘⣆⠀⢀⡴⡆
⠀⠀⣿⢻⣿⣿⣄⡸⠀⡆⠀⠒⣈⣩⣉⣉⡈⠉⠉⠢⣉⠉⠀⠀⠀⠀⠀⠀⠀⢣⠈⠢⣀⠈⠉⢁⡴⠃
⠀⢀⢿⣿⣿⡿⠛⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣸⢿⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⡇⠉⠉⠁⠀⠀
⣠⣞⠘⢛⡛⢻⣷⣤⡀⠈⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠇⢰⡇⠀⠀⠀⠀⠀
⠻⣌⠯⡁⢠⣸⣿⣿⣷⡄⠁⠈⢻⢿⣿⣿⣿⣿⠿⠋⠃⠰⣀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀
⠀⠀⠉⢻⠨⠟⠹⢿⣿⢣⠀⠀⢨⡧⣌⠉⠁⣀⠴⠊⠑⠀⡸⠛⠀⠀⠀⠀⠀⣸⢲⡟⠀⠀⠀⠀⠀⠀
⠀⠀⣠⠏⠀⠀⠀⠉⠉⠁⠀⠐⠁⠀⠀⢉⣉⠁⠀⠀⢀⠔⢷⣄⠀⠀⠀⠀⢠⣻⡞⠀⠀⠀⠀⠀⠀⠀
⠀⢠⠟⡦⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢾⠉⠀⣹⣦⠤⣿⣿⡟⠁⠀⠀⠀⢀⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠙⣦⣁⡎⢈⠏⢱⠚⢲⠔⢲⠲⡖⠖⣦⣿⡟⠀⣿⡿⠁⣠⢔⡤⠷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣟⠿⡿⠿⠶⢾⠶⠾⠶⠾⠞⢻⠋⠏⣸⠁⠀⡽⠓⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⡏⠳⠷⠴⠣⠜⠢⠜⠓⠛⠊⠀⢀⡴⠣⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣏⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⢀⣀⣀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠖⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠉⠑⠒⠒⠐⠒⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠞⠋⠁⣀⣠⣴⣶⣾⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⢻⣧⣤⣴⣿⠿⠋⠁⣴⡿⠿⢿⣿⣿⣿⣷⣶⣶⣶⣶⡶⠶⠚⠁⠀⠀⣠⣾⠏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣥⣤⣤⣭⣍⣁⡀⠀⠀⠘⣿⣇⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⢀⣠⣴⣿⠟⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⢿⣷⣦⣄⣀⣀⣀⣀⣀⣤⣤⣶⣾⣿⡿⠛⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⣩⣿⠿⠋⠁⠀⠀⣠⣶⠟⠋⠀
⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⢠⣾⡿⠃⠀⠀⠀
⠀⠀⠀⠀⣠⡟⡡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠸⣿⣄⠀⢀⣴⣿⣿⠁⠀⠀⠀⠀
⠀⠀⠀⢠⡟⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⣤⠶⠒⠛⠛⠒⠲⢤⡀⠀⠘⣷⠀⠀⠀⠙⠻⠿⠿⢿⣿⠇⠀⠀⠀⠀⠀
⠀⣠⡶⠿⢇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢀⡴⢪⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⢹⡄⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀
⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⣦⣤⡞⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⡇⠀⠀⠀⢀⣠⣾⠟⢠⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡟⣿⣆⢀⠀⠀⠀⠀⠀⣠⠾⠕⠉⢉⣉⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠃⠀⣠⣶⣿⠟⠋⢀⣾⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣿⣿⣯⣧⠠⠮⠴⠞⣁⣠⣴⣾⣿⣿⣷⡌⣿⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠉⠀⠀⣠⣾⡏⠀⠀⠀⠀⠀⠀
⠀⣠⠴⢾⣿⣿⣿⣿⠀⠳⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣤⣴⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀
⢰⠁⠀⠀⠙⣿⣿⣧⠈⡆⢻⢿⣿⣿⣿⣿⣿⠿⠟⣃⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⣼⠀⢈⣩⣽⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣞⠀⠀⠀⣠⣿⣿⡿⠀⢺⡀⢑⡈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠻⣦⡞⠀⠀⠀⠀⠀⢠⣮⣾⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⣦⣄⣴⡿⡿⠷⣿⠠⣀⡨⠥⣞⣳⡄⠀⢀⡀⠀⠀⠀⠀⠀⣀⣿⣇⠀⠀⠀⣀⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⢻⠇⠀⠀⠀⠈⠣⠀⠀⠀⠀⢀⡽⣷⣄⡈⠉⠉⠀⠀⣊⣽⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⡴⣫⣿⣿⣒⡢⢄⣠⡾⠋⠉⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⠛⣷⣤⢀⡄⢀⠇⣠⠂⣸⣡⣚⣼⠋⠁⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⣾⡀⡏⠙⡗⠻⠟⢻⠚⢻⢹⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠓⠧⠴⣇⣴⣄⢼⣤⠟⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀
⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⣿⣿
⠘⣿⣧⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⢀⣿⡏
⠀⣿⣿⡄⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⣼⣿⠃
⠀⠘⢿⣿⣦⣤⣤⣀⣀⠀⢀⣀⣀⣤⡿⡿⣧⣤⣀⠀⠀⣀⣀⣀⣤⣤⣾⣿⡏⠀
⠀⠀⠘⢿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⠃⡇⠹⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⠇⠀
⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢠⣧⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀
⠀⠀⢿⣿⣿⣿⠿⠋⠁⠀⣿⣿⣿⣧⣿⣿⣧⣾⣿⣿⣿⡏⠁⠀⠈⣻⣿⡿⠃⠀
⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⢿⣿⡿⠿⣿⣿⡇⠀⠀⠀⠛⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⠰⣿⡇⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⠰⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⣿⣿⢘⣿⡇⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣿⢈⣿⡇⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⢨⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢸⣿⢨⣿⠃⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀